AI engineering glossary · Linear algebra
What is orthogonal projection?
Orthogonal projection: A projection in which the leftover difference between the vector and its image is perpendicular to the target subspace, making the image the closest point in it. Least squares fitting is exactly this operation applied to the target vector.
Orthogonal projection: an example
The orthogonal projection of b = [1, 2, 3] onto the x-y plane is [1, 2, 0], and the leftover [0, 0, 3] is perpendicular to the plane.
Related terms
- Projection
- Projection matrix
- Least squares
- Orthogonal complement
More Linear algebra terms
- Orthogonal vectors
- Orthonormal basis
- Outer product
- Permutation matrix
- Pivot
- Positive definite matrix
- Positive semi-definite matrix
- Power iteration
Where you learn it
Orthogonal projection is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.